Answer
$x = 4$
$y = 5$
Work Step by Step
Theorem 6-6 states that in a quadrilateral that is a parallelogram, its diagonals bisect one another.
We can now deduce that for bisector $\overline{AC}$, its bisected segments are congruent to one another. For $\overline{BD}$, its bisected segments are congruent to one another. Let's set up the two equations reflecting this information:
$3y - 3 = 3x$
$4x - 2 = 3y - 1$
We can solve for both $x$ and $y$ by setting the two equations up as a system of equations. Move all variables to the left side of the equations, and move all constants to the right side of the equations:
$-3x + 3y = 3$
$4x - 3y = 1$
$x = 4$
Plug this value in to solve for y:
$3y - 3 = 3(4)$
Multiply first:
$3y - 3 = 12$
Add $3$ to each side of the equation to move constants to the right side of the equation:
$3y = 15$
Divide each side of the equation by $3$ to solve for $y$:
$y = 5$
